Correct answer: 8,4
Spin quantum number tell us about the spin of an electrons around the nucleus.It can have two values which are +1/2 and -1/2. The +1/2 value indicates clockwise spin and other indicates anti-clockwise spin of an electron.
The electronic configuration of Gd = [Xe]6s2,4f7,5d1
The configuration clearly suggest that all the electrons except 4f and 5d are paired,so the sum of spin quantum number values for these electrons will be 0(as values will be + 1/2 and -1/2 for the paired e-s). Now for 7 electrons in 4f and 1 e- in 5d i.e total of 8e-s,the sum of spin quantum no. value will be 8/2 = 4 (as these e-s are not paired so value of spin quantum no. taken as +1/2 thereby comprising of total 8/2 = 4). Now total sum will be = 4 + 0 = 4